For me, the most important lesson from Olympic-style weightlifting is that you can't cram for a competition. No amount of natural talent can make up for failing to invest the hours over the course of weeks, months and years.
I just went and read your link above. Have to say you captured my progression perfectly as well. I was a typical HNer, getting by on raw intelligence without putting in a whole bunch of effort. I am lucky that I caught this before it caught up with me professionally, but I DIDN'T catch it in my athletic endeavors. I ended up tearing an Achilles because I wasn't prepared.
Now, years later, I've applied what I learned professionally to my athletic life and am going through the same olympic stuff you talked about. Spot on. Good write up.
For me the first big lesson was that the body really needs time to recover after training hard, and the second was that training "no matter what" doesn't work if you're trying to improve maximum strength. Lifting is a neuromuscular activity requiring maximum activation, and if I'm very exhausted or sleep deprived, I won't be able to train hard enough to matter, so doing a less intense core workout and lift the next day is more reasonable.
The Bulgarian system of training is built around daily 1-rep maxes, then backing off for work sets.
The nice thing about it is that this means that if you're having a crappy day, you accept it and train what you can. If you're having an awesome day, you squeeze more out of it.
Learning to give-and-take with your "recovery budget" is definitely an important lesson. I train less hard than I'm capable of because my employers don't pay me to be a zombie.
I could go on, but I've already put my thoughts into words: http://news.ycombinator.com/item?id=3431621
There's a proverbial bit of wisdom that has been attributed to various sources: The will to win is important. The will to prepare is essential.